Three cards are lined up on a table. each card has a letter printed on one side
and a positive number printed on the other side. one card has an r printed on
it, one card has a g printed on it, and one card has a b printed on it. the
number side of each card is facedown on the table. the following is known about
the three concealed numbers:

(i) the product of the number on the card with an r and the number on the
card with a g equals the number on the card with a b;
(ii) the product of the number on the card with a g and the number on the card
with a b is 180; and
(iii) five times the number on the card with a b equals the number on the card
with a g.

determine the product of the numbers on the three cards.